BP shares enjoyed a relief rally today after it emerged that the fine it faces for its Gulf of Mexico oil disaster will be lower than feared after a judge ruled less oil was spilled than originally claimed.

The US government had estimated the 2010 fatal disaster had spilled up to 4.2million barrels of oil - but US District Judge Carl Barbier last night ruled a quarter less was actually leaked, or around 3.2million barrels.

The judge also found BP's response to the Deepwater Horizon drilling rig explosion had not been grossly negligent but he stuck to his earlier ruling that BP was grossly negligent leading up to the fatal blowout. BP has appealed that decision.

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BP set aside $42billion (£28billion) in total to cover compensation and fines arising from the fatal Deepwater Horizon drilling rig explosion in the Gulf of Mexico in 2010

The maximum £9billion ($13.7billion) penalty fine that BP now faces is less than the £11.5billion ($17.6billion) feared, although a final figure is yet to be set by the courts in New Orleans.

BP has set aside $42billion (£28billion) in total to cover compensation and fines and has been selling off assets – totalling around £25billion – since the disaster.

It has already accepted criminal responsibility for the disaster and agreed to pay $4.5billion (£3billion) to the US government.

BP’s subsidiary, BPXP (BP Exploration & Production) is being tried under the US Clean Water Act.

The third phase of the trial kicks off next week in New Orleans. Phase one and two were to assess the penalty and the third phase sets the penalty.

Judge Barbier will determine the amount of the fines, based on elements including what BP did to reduce the effects of the disaster, the economic impact of the spill and the economic impact of a fine on the company.

BP will argue that due to the falling price of oil the penalty sought by the US would have a ‘very significant negative economic impact’ on BPXP.

It will argue that the ‘economic environment in which the price of oil has dropped’ means its subsidiary would be adversely affected.

BP still faces claims by private parties and state governments including banks, casinos, local governments and businesses.

BP shares topped the FTSE 100 leader board in afternoon trade, up 3.2 per cent or 12.55p to 405.15p on some relief at the judgement and helped by a firmer oil price as Brent crude headed back towards $50 a barrel.